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Why formalize mathematics - more than catching errors

Why formalize mathematics - more than catching errors I read a good post by one of the authors of the Isabelle theorem prover, that got me thinking. The author, Lawrence Paulson, observed that most math proofs are trivial, but writing them (preferably with a proof assistant) is a worthwhile activity, for reasons similar to safety checklists - “Not every obvious statement is true.” As I have been a bit obsessed with doing formalized mathematics, this got me thinking about why I am excited to spend many hours recently writing formalized proofs in Lean for exercises from Tao’s Real Analysis (along with this recent attempt to write a companion to Riehl’s Category Theory In Context). On a very personal level, I just like math, computers and puzzles, and writing Lean proofs feels like doing all three at once. But I do believe formalization is important beyond nerd-snipping folks like me.

rkirov.github.io · Rado's Radical Reflections

Leaning on AI

Leaning on AI It’s been five months since my last dedicated Lean post and as usual I have started to lose steam on Lean projects. After the thrill of discovering the world of formalized mathematics started to wear off, I did not find motivation to push as hard as before. The SF Math with Lean work group kept me vaguely connected (at least in the one hour a week we meet (see retro)) but other than that I wasn’t putting in more than a few hours a week on math and Lean.

rkirov.github.io · Rado's Radical Reflections

Learning Lean: Part 3

I am continuing to learn Lean (see part 1 and part 2). I lost some steam around March-April, but in the last two months I picked it up again. In a way it was a nice spaced repetition for relearning some of the basics. This summary was supposed to be my notes from finishing the rest of Mathematics in Lean and finishing chapters 2 and 3 of exercises from Terence Tao’s Analysis textbook, but also I couldn’t help also comment on the challenges and opportunties I see in doing formal mathematics with Lean.

rkirov.github.io · Rado's Radical Reflections

Learning Lean: Part 2

I am continuing to learn Lean (see part 1) by going through Mathematics in Lean. These are my notes as I just finished chapters one through five. Mathematics in Lean The online book is well-paced and well-written to connect with what an average student of mathematics already knows. The focus is on learning how to do basic mathematical proofs in Lean, and the underlying language is taught as needed for those goals, in comparison to Theorem Proving in Lean which is more of a language guide. For example, the fact that naturals are constructed as an inductive type with zero and succ constructors is shown much after one is shown how to work with them. This is aligned with how a lot of mathematics is done before one discusses foundations in a typical mathematics curriculum, which might differ from a CS one.

rkirov.github.io · Rado's Radical Reflections

Oh, good: Discord's age verification rollout has ties to Palantir co-founder and panopticon architect Peter Thiel

Discord is "experimenting" with an age authentication vendor whose major investors include Thiel's Founders Fund.

www.pcgamer.com · PC Gamer

Learning Lean: Part 1

Motivation I’ve been captivated by the recent movement to popularize mathematics formalization through the Lean theorem prover, and this year I’m diving deeper into learning it. For those unfamiliar with this revolution, I highly recommend watching Kevin Buzzard’s talks on YouTube for an overview of why formal mathematics is generating such excitement in the mathematical community. The immediate benefits of formalization are well-documented: it helps catch errors in proofs and reduces the need for trust between collaborators since every step is mechanically verified. However, I believe there’s another compelling advantage that’s less frequently discussed: formalization enables a better separation of concerns in mathematical writing.

rkirov.github.io · Rado's Radical Reflections

설 연휴 이튿날, 흐리고 낮 19도 ‘봄기운’…미세먼지는 나쁨

설 연휴 둘째 날이자 일요일인 15일은 전국에 비교적 포근한 날씨가 이어지는 가운데 중부 지방을 중심으로 미세먼지가 짙게 낄 것으로 예상된다. 14일 기상청 예보를 보면, 15일 아침 최저기온은 영하 2도~7도고, 낮 최고기온은 6~19도로 예년보다 높을 것으로 전망된

www.hani.co.kr · 한겨레

"1분 늦으면 15분 치 임금 깎아"‥근로감독 결과 드러난 런베뮤의 민낯

지난해, 유명 빵집 런던베이글뮤지엄에서 20대 직원이 숨지며 장시간 근로에 시달렸다는 의혹이 불거졌는데요. 노동부가 근로 감독에 나서보니 주 80시간 넘는 근로를 시키...

imnews.imbc.com · MBC 뉴스

P03 (@p0333.bsky.social)

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bsky.app · Bluesky Social